High Energy Physics - Phenomenology · arXiv:hep-ph/0402136 v1 · submitted 12 Feb 2004
Linear sigma model at finite temperature
The paper says
“In the N=4 case, there is indication of a first-order phase transition, while in the large N approximation the phase transition appears as second-order.”
from the abstract · picked out as the main claim by a classifier
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The paper
Abstract
The chiral phase transition is investigated within the framework of thermal field theory using the O(N) linear sigma model as an effective theory. We calculate the thermal effective potential by using the Cornwall-Jackiw-Tomboulis formalism of composite operators. The thermal effective potential is calculated for N=4 involving as usual the sigma and the three pions, and in the large-N approximation involving N-1 pion fields. In both cases, the system of the resulting gap equations for the thermal effective masses of the particles has been solved numerically, and we have investigated the evolution of the effective potential. In the N=4 case, there is indication of a first-order phase transition, while in the large N approximation the phase transition appears as second-order. In this analysis, we have ignored quantum fluctuations and have used the imaginary time formalism for calculations. We have extended our calculation in order to include the full effect of two loops in the calculation of the effective potential. In this case, the effective masses are momentum dependent. In order to perform the calculations, we found the real time formalism to be convenient. We have calculated the effective masses of pions at the low-temperature phase and we found a quadratic dependence on temperature, in contrast to the Hartree case, where the mass is proportional to temperature. The sigma mass was investigated in the presence of massive pions, and we found a small deviation compared to the Hartree case. In all cases, the system approaches the behaviour of the ideal gas at the high temperature limit.
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.
abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: hedged possibility 0.91
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.31 · randomized assignment 0.01 · states quantitative result 0.26 · compares with prior results 0.94 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| The chiral phase transition is investigated within the framework of thermal field theory using the O(N) linear sigma model as an effective theory. | contribution 0.46 | 0.66 | 0.04 | asserted 0.96 |
| We calculate the thermal effective potential by using the Cornwall-Jackiw-Tomboulis formalism of composite operators. | method 0.96 | 0.93 | 0.03 | asserted 1.00 |
| The thermal effective potential is calculated for N=4 involving as usual the sigma and the three pions, and in the large-N approximation involving N-1 pion fields. | method 0.82 | 0.85 | 0.04 | asserted 1.00 |
| In both cases, the system of the resulting gap equations for the thermal effective masses of the particles has been solved numerically, and we have investigated the evolution of the effective potential. | method 0.93 | 0.96 | 0.06 | asserted 1.00 |
| In the N=4 case, there is indication of a first-order phase transition, while in the large N approximation the phase transition appears as second-order. | result 0.99 | 0.93 | 0.62 | hedged possibility 0.91 |
| In this analysis, we have ignored quantum fluctuations and have used the imaginary time formalism for calculations. | limitation 0.75 | 0.91 | 0.03 | asserted 1.00 |
| We have extended our calculation in order to include the full effect of two loops in the calculation of the effective potential. | contribution 0.94 | 0.95 | 0.05 | asserted 1.00 |
| In this case, the effective masses are momentum dependent. | result 0.93 | 0.74 | 0.04 | asserted 1.00 |
| In order to perform the calculations, we found the real time formalism to be convenient. | method 1.00 | 0.88 | 0.02 | asserted 0.99 |
| We have calculated the effective masses of pions at the low-temperature phase and we found a quadratic dependence on temperature, in contrast to the Hartree case, where the mass is proportional to temperature. | result 1.00 | 0.96 | 0.10 | asserted 1.00 |
| The sigma mass was investigated in the presence of massive pions, and we found a small deviation compared to the Hartree case. | result 1.00 | 0.96 | 0.05 | asserted 1.00 |
| In all cases, the system approaches the behaviour of the ideal gas at the high temperature limit. | result 0.98 | 0.83 | 0.17 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from simulation or computation 0.97
What was examined, and what was not
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- arXiv listing abstract v1
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- references and citing sentences
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How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 8,764 input tokens, $0.0004 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 3 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field hep-ph · Aug 2019
- Pion Superfluidity and Meson Properties at Finite Isospin Density hep-ph · Mar 2005
- Thermodynamics of QCD-inspired theories hep-ph · Apr 2006
How the literature uses it
18 arXiv papers cite this in 21 sentences
Papers citing it · 8 sentences without a confident label
Contests it 1 paper
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However, the CJT effective action in chiral limit presented in Refs. [ref] violates the Goldstone theorem and gives massive pions in the spontaneous symmetry breaking phase, besides, the temperature-dependent order parameter predicts a first order phase transition.
Pion String evolving in a thermal bath · Introduction · contest 0.92
Compares with it 1 paper
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This stands in contrast to the large-$N$ approximation, which correctly determines the order of the phase transition but gives a critical temperature larger by a factor of $√(3/2)+𝒪(N^-1)$ (see [ref] ).
Symmetry improvement of 3PI effective actions for O(N) scalar field theory · Solution of the Hartree-Fock approximation · 0.90
Cites it as background 10 papers
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The CJT formalism has been applied to study the thermodynamics of the $O(N)$ model in the so-called “double-bubble” approximation [ref] , in Ref. [ref] sunset-type diagrams have been included.
Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method · Introduction · 0.89
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Many investigations of the linear $σ$-model at nonzero $T$ have been performed in the past, see e.g. Refs. [ref] and refs. therein.
Restoration of chiral symmetry in the large-N_c limit · Introduction · 1.00
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For some works, including beyond MF corrections to the NJL model and linear sigma model see [ref] .
One-meson-loop NJL model: Effect of collective and noncollective excitations on the quark condensate at finite temperature · Introduction · 0.93
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